Dynamics of Single and Binary Black Holes in Galactic Nuclei

Galactic nuclei represent one of the most fascinating and dynamically richest regions of our Universe. They are often found to host at least one supermassive black hole (MBH) at their centre; in addition, observations suggest that MBHs frequently coexist with massive and extremely dense nuclear star clusters, making galactic nuclei ideal laboratories for the study of a broad range of exotic dynamical phenomena. This thesis aims at providing new insights on the interplay between MBHs and their host environments by means of advanced numerical techniques. In particular, my work is relevant in the landscape of gravitational waves (GWs), as it explores the dynamical evolution of stellar compact objects and MBHs: these objects are expected to be promising GW sources detectable by present and future interferometers, as the forthcoming space-borne LISA observatory. In this framework, Bortolas et al. (2017) investigates the impact of natal kicks on the distribution of compact objects in the Milky Way Galactic Centre (GC). My results show that supernova (SN) kicks typically either unbind neutron stars from the MBH, or set them on very eccentric orbits. In contrast, stellar black holes are not significantly affected by the kick: this, combined with mass segregation, would suggest a cusp of stellar relics to inhabit the GC innermost region, as supported by the recent detection of a cusp of accreting X-ray binaries near the MBH. In addition, this thesis is the first to provide evidence that SN kicks may trigger extreme mass ratio inspirals (EMRIs), i.e. GW driven decays of stellar mass compact objects onto MBHs. In Bortolas & Mapelli (2019) I show that SN kicks effectively funnel infant black holes and neutron stars on low angular momentum orbits, promoting their GW decay onto the MBH. By applying this argument to the young stars in the GC, I predict up to 0.01% of SN kicks to induce an EMRI, meaning that LISA will detect up to a few SN-driven EMRIs from Milky-Way like galaxies every year. A further relevant GW source for the LISA observatory is constituted by the coalescence of MBH binaries (BHBs). BHBs are expected to form in large numbers along the cosmic history, being a natural outcome of galaxy collisions. Their coupling in gas-poor galaxies can be described as a three-step process: a dynamical friction dominated phase, a migration phase induced by slingshot ejections of stars, and a GW driven inspiral leading to rapid coalescence. It has been pointed out that the slingshot-driven pairing may be ineffective if too few stars are scattered in the BHB vicinity, and the shrinking may come to a halt at roughly pc separation. However, there is circumstantial evidence that MBH pairs are rare and BHBs are likely to merge: this motivated a series of works aimed to solve the 'final pc problem'. This thesis contributes to the forge of possible solutions in multiple ways. In Bortolas et al. (2018a), I explore the infall of a young massive star cluster onto a BHB. I show that a cluster approaching the BHB along a non-zero angular momentum orbit fails to enhance the BHB shrinking; in contrast, the same cluster free-falling onto the BHB considerably contributes to the BHB pairing, as the BHB separation shrinks by more than 10%. This suggests that several cluster infalls may effectively bring the BHB close to the regime at which GWs lead to a prompt coalescence. A more general solution to the final pc problem is currently believed to reside in the non-sphericity (triaxiality) of the host galaxy. If the host galaxy is triaxial (e.g. as a result of a merger), large scale gravitational torques ensure that stars are continually scattered in the BHB vicinity. This assumption was initially validated via direct summation N-body simulations. However, the reliability of such simulations has been questioned due to the modest achievable number of particles (~1M). In fact, resolution limits enhance the amplitude of the BHB random walk, artificially boosting the BHB shrinking rate. In Bortolas et al. (2016), I numerically explore the significance of such spurious effect: I show that Brownian motion does not affect the evolution of BHBs in simulations including 1M particles or more, providing more reliability to the conclusion that BHBs effectively find their way to coalescence in non-spherical systems. Finally, in Bortolas et al. (2018b) I explore the interplay between the BHB dynamics and the shape of its host system. My study suggests that no strong connection exists between the galaxy morphology and the BHB shrinking rate, which seems to depend only on the inner density slope of the host galaxy. Such result is particularly relevant for GW science, as the time needed for a BHB to reach its GW-emission stage can be assumed to scale only with the central density of the nucleus. In conclusion, this thesis adds several pieces of information to our knowledge of GW sources in galactic nuclei, in preparation for the future of GW observations.